NAG Toolbox: nag_lapack_zgesdd (f08kr)

Purpose

nag_lapack_zgesdd (f08kr) computes the singular value decomposition (SVD) of a complex mm by nn matrix AA, optionally computing the left and/or right singular vectors, by using a divide-and-conquer method.

Syntax

Description

The SVD is written as

A = UΣVH,

A=UΣVH,

where ΣΣ is an mm by nn matrix which is zero except for its min(m,n)min(m,n) diagonal elements, UU is an mm by mm unitary matrix, and VV is an nn by nn unitary matrix. The diagonal elements of ΣΣ are the singular values of AA; they are real and non-negative, and are returned in descending order. The first min(m,n)min(m,n) columns of UU and VV are the left and right singular vectors of AA.

If m ≥ nm≥n, the first nn columns of UU are overwritten on the array a and all rows of VHVH are returned in the array vt. Otherwise, all columns of UU are returned in the array u and the first mm rows of VHVH are overwritten in the array vt.

Output Parameters

If jobz = 'O'jobz='O', a is overwritten with the first nn columns of UU (the left singular vectors, stored column-wise) if m ≥ nm≥n; a is overwritten with the first mm rows of VHVH (the right singular vectors, stored row-wise) otherwise.

It is possible that info refers to a parameter that is omitted from the MATLAB interface. This usually indicates that an error in one of the other input parameters has caused an incorrect value to be inferred.